We performed an EEG graph analysis on data from 31 typical readers (22.27 ± 2.53 y/o) and 24 dyslexics (22.99 ± 2.29 y/o), recorded while they were engaged in an audiovisual task and during resting-state. The task simulates reading acquisition as participants learned new letter-sound mappings via feedback. EEG data was filtered for the delta (0.5–4 Hz), theta (4–8 Hz), alpha (8–13 Hz), and beta (13–30 Hz) bands. We computed the Phase Lag Index (PLI) to provide an estimate of the (...) functional connectivity between all pairs of electrodes per band. Then, networks were constructed using a Minimum Spanning Tree (MST), a unique sub-graph connecting all nodes (electrodes) without loops, aimed at minimizing bias in between groups and conditions comparisons. Both groups showed a comparable accuracy increase during task blocks, indicating that they correctly learned the new associations. The EEG results revealed lower task-specific theta connectivity, and lower theta degree correlation over both rest and task recordings, indicating less network integration in dyslexics compared to typical readers. This pattern suggests a role of theta oscillations in dyslexia and may reflect differences in task engagement between the groups, although robust correlations between MST metrics and performance indices were lacking. (shrink)

We examine “de Broglie-Bohm” causal trajectories for the two electrons in a nonrelativistic helium atom, taking into account the spin-dependent momentum terms that arise from the Pauli current. Given that this many-body problem is not exactly solvable, we examine approximations to various helium eigenstates provided by a low-dimensional basis comprised of tensor products of one-particle hydrogenic eigenstates.First to be considered are the simplest approximations to the ground and first-excited electronic states found in every introductory quantum mechanics textbook. For example, the (...) trajectories associated with the simple 1s(1)1s(2) approximation to the ground state are, to say the least, nontrivial and nonclassical.We then examine higher-dimensional approximations, i.e., eigenstates Ψ α of the Hamiltonian in this truncated basis, and show that ∇ i S α =0 for both particles, implying that only the spin-dependent momentum term contributes to electronic motion. This result is independent of the size of the truncated basis set, implying that the qualitative features of the trajectories will be the same, regardless of the accuracy of the eigenfunction approximation.The electronic motion associated with these eigenstates is quite specialized due to the condition that the spins of the two electrons comprise a two-spin eigenfunction of the total spin operator. The electrons either (i) remain stationary or (ii) execute circular orbits around the z-axis with constant velocity. (shrink)

The metaphor is derived from archery. The epithet πτερόες is appropriate to arrows [πτερόεντες ỏịστοί E 171, ỉờν βλτα πτερόεντα Δ 117, οì πτερόεντες π 773, πτερόεντα 68]. Just as πτερόεντα means ‘feathered arrows,’ so πεα πτερόεντα means ‘feathered words.’ The early Greeks, when they formed a picture of words in their minds, thought of them as missiles—not as birds. Whence ‘to utter’ words is ένα or ένα. Missiles so light are more readily imagined as arrows than as spears or (...) stones. (shrink)